Earlier, the ABF had said it would be checking people's visas on the streets of the city centre as part of the operation, which also involved Victoria Police and other agencies.

The original announcement quoted ABF regional commander for Victoria and Tasmania Don Smith as saying officers would be positioned at various locations around the city and would speak "with any individual we cross paths with".

The ABF then issued another statement saying: "To be clear, the ABF does not and will not stop people at random in the streets ... the ABF does not target of the basis of race, religion, or ethnicity".

More details were expected to be released in a press conference at 2:00pm on Friday, but the event was cancelled after demonstrators began assembling outside Melbourne's Flinders Street Station to protest against the operation.

"We were advised it would target anti-social behaviour and commuters to ensure people got home safely."

The Victorian Government said Operation Fortitude was "intended to be a standard police operation".

"We fully support the decision by Victoria Police to cancel the operation after the unfortunate and inappropriate characterisation by the Australian Border Force today."

Shadow Minister for Immigration and Border Protection Richard Marles called on Mr Dutton to explain how the operation went wrong.

"Immigration Minister Peter Dutton needs to come out of hiding and provide an explanation for the shambles that has seen a cross agency operation compromised and a key Government agency left red faced," he said in a statement.

"This has been incredibly badly handled and Peter Dutton needs to immediately come clean on how this announcement was so botched.

"Who sanctioned this announcement being made, what was its purpose, who called for its retraction and who is responsible for compromising this operation?"

"Joseph Stalin would be proud of Tony Abbott," he said in a statement.

"Just as East Germany's Stasi would be delighted with the Australian Border Force — why, even [Chilean dictator] General Pinochet would be impressed.

"The decision by the Federal Government to cancel this weekend's security operation in Melbourne is a welcome respite, for now at least, but the Government has shown its hand by planning the operation in the first place.

He said the community was right to protest the Government's actions, saying it was turning Australia into a "police state".